My club, Orpheus, receives a number of enquiries every year and these can vary tremendously.
Some are from people who have never tried caving but want to have a go - so we are able to lend them kit and take them on a relatively simple trip, ensuring they have Temporary BCA Membership (which lasts for 3 months and up to 4 weekend/trips) and we also give them information on how they can go on to join the Club. A few of these do stay on and join but most seem to be trying a number of different "adventure sports" and after just one trip decide caving isn't for them.
We also have an increasing number of people referred to us who have tried caving with a local Outdoor Pursuits organisation and want to do more: these we find do tend to want to stick with it and join as Prospective Members within their 3 months' trial. Some of these are young people and, since the Club decided a few years ago that we could allow under-16's as Junior Members, we have been able to help them. However, we do expect that their parents will be involved in all caving trips as we don't currently have any club members with appropriate CRB checks or other qualifications. (All but one of our Junior Members has now progressed to become an adult Full Member but we are still happy to take on juniors.)
We are also finding a number of older people contact us to say that they were cavers in their youth, or at university, and dropped out but now have more spare time and want to take it up again seriously. These come with a definite idea of rejoining the caving scene and most become Members fairly quickly.
In the past we have found that many people who joined as older teenagers lasted only two or three years as keen cavers, specialising in the hardest and deepest caves, and once they'd cracked all the really tough trips, dropped out of caving altogether as they acquired jobs which took up more time, got married, etc. One or two of of these have now returned to the fold, retaining fond memories of their time as active cavers.
As Andy points out, there are many more adventurous activities for people to try out which simply didn't exist even a few years ago. Many of these are high-profile, involve brightly coloured clothes or equipment and are very "visible" to spectators - these attract young people in a way that caving never can. The other point is that those who stick with caving often go on to take an interest in a particular aspect of caving which adds to their enjoyment: surveying, digging, amateur research, photography, etc. They almost always take a keen interest in cave conservation because they are in it for the long term and have seen the damage that can be done by thoughless behaviour or sheer pressure of numbers. So some might consider it's in our own interest not to attract too many new cavers?